Probability Explanation And Exercises Worksheet Page 7
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37Table 1. 36 possible outcomes.
Die 1
Die 2
Total
Die 1
Die 2
Total
Die 1
Die 2
Total
1
1
2
3
1
4
5
1
6
1
2
3
3
2
5
5
2
7
1
3
4
3
3
6
5
3
8
1
4
5
3
4
7
5
4
9
1
5
6
3
5
8
5
5
10
1
6
7
3
6
9
5
6
11
2
1
3
4
1
5
6
1
7
2
2
4
4
2
6
6
2
8
2
3
5
4
3
7
6
3
9
2
4
6
4
4
8
6
4
10
2
5
7
4
5
9
6
5
11
2
6
8
4
6
10
6
6
12
You can see that 5 of the 36 possibilities total 6. Therefore, the probability is 5/36.
If you know the probability of an event occurring, it is easy to compute the
probability that the event does not occur. If P(A) is the probability of Event A, then
1 - P(A) is the probability that the event does not occur. For the last example, the
probability that the total is 6 is 5/36. Therefore, the probability that the total is not
6 is 1 - 5/36 = 31/36.
Probability of Two (or more) Independent Events
Events A and B are independent events if the probability of Event B occurring is
the same whether or not Event A occurs. Let's take a simple example. A fair coin is
tossed two times. The probability that a head comes up on the second toss is 1/2
regardless of whether or not a head came up on the first toss. The two events are
(1) first toss is a head and (2) second toss is a head. So these events are
independent. Consider the two events (1) “It will rain tomorrow in Houston” and
(2) “It will rain tomorrow in Galveston” (a city near Houston). These events are
not independent because it is more likely that it will rain in Galveston on days it
rains in Houston than on days it does not.
191
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